Most connectionist parsers either cannot guarantee the correctness of their derivations or have to simulate a serial flow of control. In the first case, users have to restrict the tasks (e.g. parse less complex or shorter sentences) of the parser or they need to believe in the soundness of the result. In the second case, the resulting network has lost most of its attractivity because seriality needs to be hard-coded into the structure of the net. We here present a hybrid symbolic connectionist parser, which was designed to fulfill the following goals: (1) parsing of sentences without length restriction, (2) soundness and completeness for any context-free grammar, and (3) learning the applicability of parsing rules with a neural network. Our hybrid architecture consists of a serial parsing algorithm and a trainable net. BrainC (Backtracking and Backpropagation in C) combines the well known shift-reduce parsing technique with backtracking with a backpropagation network to learn and represent the typical properties of the trained natural language grammars. The system has been implemented as a subsystem of the Rochester Connectionist Simulator (RCS) on SUN- Workstations and was tested with several grammars for English and German. We discuss how BrainC reached its design goals and what results we observed.